Problem: Simplify the following expression: $\dfrac{96p^5}{64p}$ You can assume $p \neq 0$.
Solution: $ \dfrac{96p^5}{64p} = \dfrac{96}{64} \cdot \dfrac{p^5}{p} $ To simplify $\frac{96}{64}$ , find the greatest common factor (GCD) of $96$ and $64$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $64 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(96, 64) = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32 $ $ \dfrac{96}{64} \cdot \dfrac{p^5}{p} = \dfrac{32 \cdot 3}{32 \cdot 2} \cdot \dfrac{p^5}{p} $ $\phantom{ \dfrac{96}{64} \cdot \dfrac{5}{1}} = \dfrac{3}{2} \cdot \dfrac{p^5}{p} $ $ \dfrac{p^5}{p} = \dfrac{p \cdot p \cdot p \cdot p \cdot p}{p} = p^4 $ $ \dfrac{3}{2} \cdot p^4 = \dfrac{3p^4}{2} $